Solutions to the First Order Difference Equations in the Multivariate Difference Field
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929223553253376 |
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| author | Du, Lixin Wei, Yarong |
| author_facet | Du, Lixin Wei, Yarong |
| contents | The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference field, in which the summation problem could be transformed into solving the first order difference equations. We then show a criterion for deciding whether the difference equation has a rational solution and present an algorithm for computing one rational solution of such a difference equation, if it exists. Moreover we get the rational solution set of such an equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions to the First Order Difference Equations in the Multivariate Difference Field Du, Lixin Wei, Yarong Combinatorics The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference field, in which the summation problem could be transformed into solving the first order difference equations. We then show a criterion for deciding whether the difference equation has a rational solution and present an algorithm for computing one rational solution of such a difference equation, if it exists. Moreover we get the rational solution set of such an equation. |
| title | Solutions to the First Order Difference Equations in the Multivariate Difference Field |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.13933 |